Question

The discriminant value of a quadratic function is 3. How many REAL solutions does the function have?

a.) 3

b.) 1

c.) 2

d.) 0

Answer 1

The answers is D. ) 0

Answer 2

This function would have two distinct real roots.

Explanation:

Consider a quadratic function
`f(x) = a\, x^(2) + b\, x + c`.

The determinant of this function would be
`\Delta = b^(2) - 4\, a\, c`.

The (only) two roots of this quadratic function would be:

`\begin{aligned} x_(1) = (-b - √(\Delta))/(2\, a)\end{aligned}`, and

`\begin{aligned} x_(2) = (-b + √(\Delta))/(2\, a)\end{aligned}`.

Because of the square root
`√(\Delta)` in the two expressions,
`x_(1)` and
`x_(2)` would take real values if and only if
`\Delta \ge 0` (determinant is nonnegative.) If
`\Delta < 0`, this quadratic function would not have any real root.

Since the only difference between the two roots
`x_(1)` and
`x_(2)` is
`(1/a)\, √(\Delta)`, these two roots would repeat one another if
`\Delta = 0` (determinant is zero.)

Otherwise, if
`\Delta > 0`, this quadratic function would have two distinct real roots.